On Saha's equation for partially ionised plasmas and Onsager's bookkeeping rule

In this work we study several definitions of free and bound states in plasmas and the consequences of Onsager's bookkeeping rule for the thermodynamic functions. In particular we investigate Onsager's rule of balance between the contributions of free and bound charges. We show that this rule guarantees at low densities the independence (stationarity) with respect to the fine details of the definition of bound states (chemical species). The Brillouin-Planck-Larkin atomic partition function which is the most natural choice is modified and the consequences of such changes are investigated. We study the free energy landscape in dependence on different choices of the mass action constant and formulate the condition of stationarity with respect to free parameters. We show that at high densities the condition of stationarity is violated (except in certain saddle points) so that in general the chemical description of plasmas can be applied only with great care.